Final answer:
None of the provided options (a) 405 (b) 413 (c) 420 (d) 428 match the correctly calculated 66th term of the arithmetic sequence, which is 653. This might indicate an error in the question's options or in the sequence provided.
Step-by-step explanation:
To find the 66th term of the arithmetic sequence given by 3, 13, 23, ..., we can use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where a1 is the first term and d is the common difference between the terms. In this sequence, a1 = 3 and the common difference d is 10, as we can see by subtracting any term from the one following it (for example, 13 - 3 = 10). Thus, the 66th term is a66 = 3 + (66 - 1) × 10 = 3 + 65 × 10 = 3 + 650 = 653. However, since none of the provided options match 653, there might be an error in the options or in the application of the arithmetic sequence formula.